In systemic lupus erythematosus (SLE), certain white blood cells called lymphocytes make substances that cause inflammation in the body's own tissues. These substances are called anti-dsDNA antibodies (anti- dsDNA), and they have been shown to be associated with SLE kidney disease. The investigational drug to be tested in this clinical trial is called LJP 394. This drug is designed to attach to anti-dsDNA antibodies and remove them from the circulation. The drug will also attach to antibodies on certain white blood cells involved in causing immune diseases, including SLE. When given to a type of mouse that has lupus, LJP 394 reduced the numbers of anti-dsDNA antibodies in the blood and markedly decreased the severity of the kidney disease. When LJP 394 was given to lupus patients in earlier studies, anti-dsDNA antibodies were decreased. The purpose of this clinical research trial is to evaluate the ability of the experimental drug to lower the amount of anti-dsDNA antibodies in the blood, to help prevent damage to the kidneys by the anti-dsDNA antibodies, and to decrease the amount of other drugs required to control the disease.